Question

A can do a certain job in 12 days. B is 60% more efficient than A. What is the number of days it takes B to do the same piece of work?
[a] 5
[b] 7.5
[c] 9.5
[d] 10

Answer 1

Hint: Find the fraction of the total work A does in one day. Hence find the fraction of the total work B does in one day. Hence find the total number of days it takes B to finish the job. Verify your answer.

Complete step-by-step answer:
A completes one job in 12 days.
Hence the fraction of job completed by A in 1 day $=\dfrac{1}{12}$.
Since B is 60% more efficient than A, the fraction of the total job completed on one day by B will be 60% more than that of A.
Hence the fraction of the total job completed by B on one day $=\dfrac{1}{12}+\dfrac{60}{100}\times \dfrac{1}{12}=\dfrac{5+3}{60}=\dfrac{8}{60}=\dfrac{2}{15}$
Hence the total number of days in which B can finish the job is $\dfrac{1}{\dfrac{2}{15}}=\dfrac{15}{2}=7.5$
Hence B finishes the job in 7.5 days.
Hence option [b] is correct.

Note: Verification:
One day work of A = $\dfrac{1}{12}th$ of total work
One day work of B $=\dfrac{1}{7.5}th=\dfrac{2}{15}th$ of total work.
Efficiency of B over A $=\dfrac{\dfrac{2}{15}-\dfrac{1}{12}}{\dfrac{1}{12}}\times 100=\dfrac{8-5}{5}\times 100=60%$
Hence B is 60% more efficient than A.
Hence our answer is verified to be correct.